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<divclass="title">sat/lp_utils.h</div></div>
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<ahref="sat_2lp__utils_8h.html">Go to the documentation of this file.</a><divclass="fragment"><divclass="line"><aname="l00001"></a><spanclass="lineno"> 1</span> <spanclass="comment">// Copyright 2010-2018 Google LLC</span></div>
<divclass="line"><aname="l00002"></a><spanclass="lineno"> 2</span> <spanclass="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
<divclass="line"><aname="l00003"></a><spanclass="lineno"> 3</span> <spanclass="comment">// you may not use this file except in compliance with the License.</span></div>
<divclass="line"><aname="l00004"></a><spanclass="lineno"> 4</span> <spanclass="comment">// You may obtain a copy of the License at</span></div>
<divclass="line"><aname="l00008"></a><spanclass="lineno"> 8</span> <spanclass="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<divclass="line"><aname="l00009"></a><spanclass="lineno"> 9</span> <spanclass="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
<divclass="line"><aname="l00010"></a><spanclass="lineno"> 10</span> <spanclass="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<divclass="line"><aname="l00011"></a><spanclass="lineno"> 11</span> <spanclass="comment">// See the License for the specific language governing permissions and</span></div>
<divclass="line"><aname="l00012"></a><spanclass="lineno"> 12</span> <spanclass="comment">// limitations under the License.</span></div>
<divclass="line"><aname="l00014"></a><spanclass="lineno"> 14</span> <spanclass="comment">// Utility functions to interact with an lp solver from the SAT context.</span></div>
<divclass="line"><aname="l00029"></a><spanclass="lineno"> 29</span> <spanclass="comment">// Returns the smallest factor f such that f * abs(x) is integer modulo the</span></div>
<divclass="line"><aname="l00030"></a><spanclass="lineno"> 30</span> <spanclass="comment">// given tolerance relative to f (we use f * tolerance). It is only looking</span></div>
<divclass="line"><aname="l00031"></a><spanclass="lineno"> 31</span> <spanclass="comment">// for f smaller than the given limit. Returns zero if no such factor exist.</span></div>
<divclass="line"><aname="l00033"></a><spanclass="lineno"> 33</span> <spanclass="comment">// The complexity is a lot less than O(limit), but it is possible that we might</span></div>
<divclass="line"><aname="l00034"></a><spanclass="lineno"> 34</span> <spanclass="comment">// miss the smallest such factor if the tolerance used is too low. This is</span></div>
<divclass="line"><aname="l00035"></a><spanclass="lineno"> 35</span> <spanclass="comment">// because we only rely on the best rational approximations of x with increasing</span></div>
<divclass="line"><aname="l00039"></a><spanclass="lineno"> 39</span> <spanclass="comment">// Multiplies all continuous variable by the given scaling parameters and change</span></div>
<divclass="line"><aname="l00040"></a><spanclass="lineno"> 40</span> <spanclass="comment">// the rest of the model accordingly. The returned vector contains the scaling</span></div>
<divclass="line"><aname="l00041"></a><spanclass="lineno"> 41</span> <spanclass="comment">// of each variable (will always be 1.0 for integers) and can be used to recover</span></div>
<divclass="line"><aname="l00042"></a><spanclass="lineno"> 42</span> <spanclass="comment">// a solution of the unscaled problem from one of the new scaled problems by</span></div>
<divclass="line"><aname="l00043"></a><spanclass="lineno"> 43</span> <spanclass="comment">// dividing the variable values.</span></div>
<divclass="line"><aname="l00045"></a><spanclass="lineno"> 45</span> <spanclass="comment">// We usually scale a continuous variable by scaling, but if its domain is going</span></div>
<divclass="line"><aname="l00046"></a><spanclass="lineno"> 46</span> <spanclass="comment">// to have larger values than max_bound, then we scale to have the max domain</span></div>
<divclass="line"><aname="l00047"></a><spanclass="lineno"> 47</span> <spanclass="comment">// magnitude equal to max_bound.</span></div>
<divclass="line"><aname="l00049"></a><spanclass="lineno"> 49</span> <spanclass="comment">// Note that it is recommended to call DetectImpliedIntegers() before this</span></div>
<divclass="line"><aname="l00050"></a><spanclass="lineno"> 50</span> <spanclass="comment">// function so that we do not scale variables that do not need to be scaled.</span></div>
<divclass="line"><aname="l00052"></a><spanclass="lineno"> 52</span> <spanclass="comment">// TODO(user): Also scale the solution hint if any.</span></div>
<divclass="line"><aname="l00056"></a><spanclass="lineno"> 56</span> <spanclass="comment">// To satisfy our scaling requirements, any terms that is almost zero can just</span></div>
<divclass="line"><aname="l00057"></a><spanclass="lineno"> 57</span> <spanclass="comment">// be set to zero. We need to do that before operations like</span></div>
<divclass="line"><aname="l00058"></a><spanclass="lineno"> 58</span> <spanclass="comment">// DetectImpliedIntegers(), becauses really low coefficients can cause issues</span></div>
<divclass="line"><aname="l00059"></a><spanclass="lineno"> 59</span> <spanclass="comment">// and might lead to less detection.</span></div>
<divclass="line"><aname="l00062"></a><spanclass="lineno"> 62</span> <spanclass="comment">// This will mark implied integer as such. Note that it can also discover</span></div>
<divclass="line"><aname="l00063"></a><spanclass="lineno"> 63</span> <spanclass="comment">// variable of the form coeff * Integer + offset, and will change the model</span></div>
<divclass="line"><aname="l00064"></a><spanclass="lineno"> 64</span> <spanclass="comment">// so that these are marked as integer. It is why we return both a scaling and</span></div>
<divclass="line"><aname="l00065"></a><spanclass="lineno"> 65</span> <spanclass="comment">// an offset to transform the solution back to its original domain.</span></div>
<divclass="line"><aname="l00067"></a><spanclass="lineno"> 67</span> <spanclass="comment">// TODO(user): Actually implement the offset part. This currently only happens</span></div>
<divclass="line"><aname="l00068"></a><spanclass="lineno"> 68</span> <spanclass="comment">// on the 3 neos-46470* miplib problems where we have a non-integer rhs.</span></div>
<divclass="line"><aname="l00072"></a><spanclass="lineno"> 72</span> <spanclass="comment">// Converts a MIP problem to a CpModel. Returns false if the coefficients</span></div>
<divclass="line"><aname="l00073"></a><spanclass="lineno"> 73</span> <spanclass="comment">// couldn't be converted to integers with a good enough precision.</span></div>
<divclass="line"><aname="l00075"></a><spanclass="lineno"> 75</span> <spanclass="comment">// There is a bunch of caveats and you can find more details on the</span></div>
<divclass="line"><aname="l00076"></a><spanclass="lineno"> 76</span> <spanclass="comment">// SatParameters proto documentation for the mip_* parameters.</span></div>
<divclass="line"><aname="l00081"></a><spanclass="lineno"> 81</span> <spanclass="comment">// Converts an integer program with only binary variables to a Boolean</span></div>
<divclass="line"><aname="l00082"></a><spanclass="lineno"> 82</span> <spanclass="comment">// optimization problem. Returns false if the problem didn't contains only</span></div>
<divclass="line"><aname="l00083"></a><spanclass="lineno"> 83</span> <spanclass="comment">// binary integer variable, or if the coefficients couldn't be converted to</span></div>
<divclass="line"><aname="l00084"></a><spanclass="lineno"> 84</span> <spanclass="comment">// integer with a good enough precision.</span></div>
<divclass="line"><aname="l00088"></a><spanclass="lineno"> 88</span> <spanclass="comment">// Converts a Boolean optimization problem to its lp formulation.</span></div>
<divclass="line"><aname="l00092"></a><spanclass="lineno"> 92</span> <spanclass="comment">// Changes the variable bounds of the lp to reflect the variables that have been</span></div>
<divclass="line"><aname="l00093"></a><spanclass="lineno"> 93</span> <spanclass="comment">// fixed by the SAT solver (i.e. assigned at decision level 0). Returns the</span></div>
<divclass="line"><aname="l00094"></a><spanclass="lineno"> 94</span> <spanclass="comment">// number of variables fixed this way.</span></div>
<divclass="line"><aname="l00097"></a><spanclass="lineno"> 97</span> <spanclass="comment">// Solves the given lp problem and uses the lp solution to drive the SAT solver</span></div>
<divclass="line"><aname="l00098"></a><spanclass="lineno"> 98</span> <spanclass="comment">// polarity choices. The variable must have the same index in the solved lp</span></div>
<divclass="line"><aname="l00099"></a><spanclass="lineno"> 99</span> <spanclass="comment">// problem and in SAT for this to make sense.</span></div>
<divclass="line"><aname="l00101"></a><spanclass="lineno"> 101</span> <spanclass="comment">// Returns false if a problem occurred while trying to solve the lp.</span></div>
<divclass="line"><aname="l00106"></a><spanclass="lineno"> 106</span> <spanclass="comment">// Solves the lp and add constraints to fix the integer variable of the lp in</span></div>
<divclass="line"><aname="l00107"></a><spanclass="lineno"> 107</span> <spanclass="comment">// the LinearBoolean problem.</span></div>
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